If we suppose the difference of temperatures between source and refrigerator to be finite, T － T', say, then since T is the temperature of the source, we have for the efficiency (T － T')⧸T. If the heat taken in be H, the heat rejected is HT'⧸T, so that the heat received by the engine is to the heat rejected by it in the ratio of T' to T. Thus, as was done by Thomson, we may define the temperatures of the source and refrigerator as proportional to the heat taken in from the source and the heat rejected to the refrigerator by a perfect engine, working between those temperatures. The scale may be made to have 100 degrees between the temperature of melting ice and the boiling point, as already explained. We shall return to the comparison of this scale with that of the air thermometer. At present we consider some of the thermodynamic relations of the properties of bodies arrived at by Thomson. First we take the working substance of the engine as consisting of matter in two states or phases; for example, ice and water, or water and saturated steam. Let us apply equation (A) to this case. If v₁, v₂ be the volume of unit of mass in the first and second states respectively, the isothermal expansion of the first part of the cycle will take place in consequence of the conversion of a mass dm from the first state to the second. Thus dv, the change of volume, is dm(v₂ － v₁). Also if L be the latent heat of the substance in the second state, _e.g._ the latent heat of water, Mdv = Ldm; so that M(v₂ － v₁) = L. If dp be the step of pressure corresponding to the step dT of temperature, equation (A) becomes dT⧸T = dp(v₂ － v₁)⧸L ... (B) In the case of coexistence of the liquid and solid phases, this gives us the very remarkable result that a change of pressure dp will raise or lower the temperature of coexistence of the two phases, that is, the melting point of the solid, by the difference of temperature, dT, according as v₂ is greater or less than v₁ Thus a substance like water, which expands in freezing, so that v₂ － v₁ is negative, has its freezing point lowered by increase of pressure and raised by diminution of pressure. This is the result predicted by Professor James Thomson and verified experimentally by his brother (p. 113 above). On the other hand, a substance like paraffin wax, which contracts in solidifying, would have its melting point raised by increase of pressure and lowered by a diminution of pressure. The same conclusions would be applicable when the phases are liquid and vapour of the same substance, if there were any case in which v₂ － v₁ is negative. As it is we see, what is well known to be the case, that the temperature of equilibrium of a liquid with its vapour is raised by increase of pressure.